Basic math
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Basic Math. Significant Figures and Scientific Notation. Significant Figures. How long is the snake ?. 1m. 1m. 0.1m = 10 cm. 1m. 0.01m = 1 cm. Significant Figures. How long is the snake ?. 0.3 m. 1m. 0.27 m. 1m. 0.1m = 10 cm. 0.270 m. 1m. 0.01m = 1 cm.

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Basic Math

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Basic math

Basic Math

Significant Figures and Scientific Notation


Significant figures

Significant Figures

How long is the snake ?

1m

1m

0.1m = 10 cm

1m

0.01m = 1 cm


Significant figures1

Significant Figures

How long is the snake ?

0.3 m

1m

0.27 m

1m

0.1m = 10 cm

0.270 m

1m

0.01m = 1 cm


Basic rules for significant digits

Basic Rules for Significant Digits

  • Rule 1- which digits are significant: The digits in a measurement that are considered significant are

    • all of those digits that represent marked calibrations on the measuring device plus one additional

    • digit to represent the estimated digit (tenths of the smallest calibration).


Adding and subtracting

Adding and Subtracting

  • The sum or difference of measurements may have no more decimal places than the least number of places in any measurement.

Ans: 29.8 m


Multiply and divide

Multiply and Divide

  • When multiplying or dividing, the number of significant figures retained may not exceed the least number of digits in either the of the factors.

0.304 cm x 73.84168 cm =

22.4 cm2

Note: only display three (3) significant figures because 0.304 only has threesignificant figures.


Big numbers

Big Numbers

  • What is the number:

    602,214,150,000,000,000,000,000

  • Avogadro’s number.

  • How do we usually see this?

    6.0221415x1023

    or

    6.0221415e+23

  • Why do we display it in this form?


Physics big and little numbers

Physics Big and Little Numbers

  • Gravitational Constant (very small)

    6.67 × 10-11 C = 6.67e-11

  • Coulomb’s Constant (very big):

    8.99 × 109 = 8.99e+9

  • Charge on an electron (very small)

    1.60217646 × 10-19 = 1.602e-19


Entering scientific notation on calculator

Entering Scientific Notation on Calculator

  • Practice with gravitational constant:

    6.67e-11

  • Type “6.67”

  • Type “2nd-,”

  • Type Negative

    (NOT minus) 11

6.67

6.67E

6.67E-11


Practice problems

Practice Problems

  • Force between two large bodies:

239 N


Practice problems1

Practice Problems

  • Force between two charges:


Unit conversions

Unit Conversions

Importance of Units and how to convert between Units


Review conversions to from scientific notation

Review: Conversions to/from Scientific Notation

  • Convert 3,600,000 to scientific notation

    • 3.6E6 or 3.6 x 106

  • Convert 0.00435 to scientific notation

    • 4.35e-3 or 4.35 x 10-3

  • Convert 8.99E9 (or 8.99 x 109)to standard notation

    • 8,990,000,000

  • Convert 6.67E-5 (or 6.67 x 10-5) to standard notation

    • 0.0000667


Why do we use units

Why do we use units?

  • Someone wants to sell you a car for 100.

    • Is this a good deal?

  • You cannot determine if this is a good deal unless you know the units.

    • $1k units ($100,000 for a car? – too high)

    • $1 units ($100 – probably pretty good)

    • $10 units ($1,000 – depends on car)

    • $0.01 (i.e. 1¢) – ($1.00 for car – great deal!)


Units cont d

Units (cont’d)

  • There are seven (7) base units in the SI system. All other units are derived from these.

    • How many can you name?


Units

Units


Units cont d1

Units (cont’d)


Basic math

acceleration

force

frequency

volume

velocity

velocity


Units prefixes

Units Prefixes


Converting units

Converting units

  • What if someone wanted to sell you their car for 5,000 £ (British pounds). Is this a good deal?

  • We need to convert units

  • We can convert units because

    • it is always okay to multiply something by 1.

    • Any number divided by itself (or its equivalent) is always equal to 1

    • As long as numerator and denominator are equivalent, the number is equal to 1.

    • $1.5782 is equal to 1 £. How much is 5,000 £ ?

    • $1 is equal to 0.6336 £. Does this change the conversion?


Converting units1

Converting Units

OR


More on converting units

More on Converting Units

  • Always okay to multiply by 1

  • We are NEVER changing the original quantity (just the way we look at it)

    • Which is more $1 or 100¢ ?

  • Ensure the undesirable units ‘cancel out’

    • One instance should be in numerator (top)

    • Other instance should be in denominator (bottom)


Practice

Practice:

  • The distance to San Antonio is 197 miles. How many km is this? (1 km = 0.62 miles)

    • 318 km

  • A sack of cement is 50 kg. How heavy is this in lbs (1 kg = 2.2 lbs)

    • 110 lbs

  • The speed limit is 65 mph. How fast is this in km/hr (1 mph = 1.60934 km/hr)

    • 105 km/hr


More complicated practice

More Complicated practice

  • How many seconds in a day?

    • 86,400

  • How many seconds in 3:45:15?

    • 13,515


More complicated practice cont d

More Complicated practice (cont’d)

  • A dropped object achieves a speed of 39.8 m/s. How fast is that in mph? (there are 1.60934 km in 1 mile).


Practice1

Practice

  • VesnaVulovic survived the longest fall on record without a parachute when her plane exploded and she fell 6miles, 551 yards. What is the distance in meters? (there are 1.60934 km in 1 mile, and 1inch = 2.54 cm).


Practice2

Practice

  • Bicyclists in the Tour de France reach speeds of 34.0 miles per hour (mi/h) on flat sections of the road. What is this speed in (a) kilometers per hour (km/h) and (b) meters per second (m/s)?


Practice3

Additional Practice available from worksheets

practice


Functions

Functions

Using functions and using basic algebra to manipulate functions


Solving physics problems

Solving Physics Problems

1. Read the problem carefully.

2. Identify the quantity to be found.

3. Identify the quantities that are given in the problem.

4. Identify the equation that contains these quantities.

5. Solve the equation for the unknown.

6. Substitute the value given in the problem, along with their proper units, into the equation and solve it.

7. Check to see if the answer will be correct in the correct units. (dimensional analysis)

8. Check your answer to see if it reasonable.


Plug and chug

Plug and Chug

  • Simply plugging in the numbers represented by the variables

  • And calculating the desired result

  • Must put the equation in the “proper” form before you can do this

    • Rearrange the formula so that the desired variable is all by itself on the left:

    • i.e. Y= {some messy equation}


Practice using formula charts

Practice – Using Formula Charts

  • Use appropriate formula to calculate “average velocity” if an object moves a distance of 923 miles in 14 hours. (you can leave the answer in mph)


Practice using formula charts1

Practice – Using Formula Charts

  • Use the appropriate formula to calculate net force that is applied if a mass of 3,900 kg (a Hummer) is accelerated 2.43 m/s2 .

    • 9501 kg·m/s2

  • Use the appropriate formula to calculate the acceleration required to move an object with an initial velocity (vi) of 0 m/s, a final velocity (vf) of 26.8 m/s, over a displacement (Δd) of 147.4 m.

    • 2.43 m/s2


Rearranging simple functions

Rearranging simple functions

  • Sometimes the desired variable is in the wrong place, so we must “solve” for the desired variable (get it all by itself and on top)

  • On simple formulas we can Cross multiply

    • This works because we can always multiply each side of function by same number


Applying to velocity time distance

Applying to Velocity/Time/Distance

  • Use formula charts

  • Show that there is “one” function

  • Create two (2) additional ones


Variable triangles

Variable Triangles

  • If you are planning on a scientific/math oriented career (including business medical fields, computers) – need to master basic algebra skills (including formula manipulations)


Variable triangles practice

Variable Triangles - practice

  • Can create for any ‘proportional’ equation


Variable triangles practice1

Variable Triangles - practice

  • Awkward and does not really work for added variables or complex equations


Practice4

Practice

  • Solve the following equation for displacement (Δd). Then solve for time (Δt).


Rearranging simple functions1

Rearranging simple functions

  • Moving a value

    • always can add to one side, if we add the same to the other side

    • Always can subtract from one side if we subtract same from the other side

  • Solve for x:


Using rearranged functions

Using “rearranged” functions

  • Using the averaged velocity function, solve the following:

    • The average velocity of the speed of light is 3e8 m/s. It takes 8 minutes (8*60 seconds) for light to reach the earth from the sun. How far is the sun?

      • 144,000,000 km

    • If Michael Phelps swims 1.667 m/s for 2 minutes (120 seconds), how far has he swam?

      • 200 m


Advanced practice

Advanced Practice

  • Solve for vi =


Advanced practice1

Advanced Practice

  • Solved for vi=

  • Or:


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